OFFSET
1,3
COMMENTS
A162320 is the array without the base 1 number lengths, and with the lengths of base 2 numbers in the top row.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10440 (covers bases 1..144)
EXAMPLE
From Michael De Vlieger, Jan 02 2015: (Start)
Array read by antidiagonals begins:
1;
1, 2;
1, 2, 3;
1, 1, 2, 4;
1, 1, 2, 3, 5;
1, 1, 1, 2, 3, 6;
1, 1, 1, 2, 2, 3, 7;
1, 1, 1, 1, 2, 2, 3, 8;
1, 1, 1, 1, 2, 2, 2, 4, 9;
1, 1, 1, 1, 1, 2, 2, 2, 4, 10;
...
Array adjusted such that the rows represent base n and the columns m:
m
1 2 3 4 5 6 7 8 9 10
------------------------------
base 1: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10;
base 2: 1, 2, 2, 3, 3, 3, 3, 4, 4, (4);
base 3: 1, 1, 2, 2, 2, 2, 2, 2, (3, 3);
base 4: 1, 1, 1, 2, 2, 2, 2, (2, 2, 2);
base 5: 1, 1, 1, 1, 2, 2, (2, 2, 2, 2);
base 6: 1, 1, 1, 1, 1, (2, 2, 2, 2, 2);
base 7: 1, 1, 1, 1, (1, 1, 2, 2, 2, 2);
base 8: 1, 1, 1, (1, 1, 1, 1, 2, 2, 2);
base 9: 1, 1, (1, 1, 1, 1, 1, 1, 2, 2);
base 10: 1, (1, 1, 1, 1, 1, 1, 1, 1, 1);
...
For n = 12, a(12) is found in the second position in row 5 in the array read by antidiagonals. This equates to m = 2, base n = 4. The number m = 2 in base n = 4 requires 1 digit, thus a(12) = 1.
For n = 14, a(14) is found in the fourth position in row 5 in the array read by antidiagonals. This equates to m = 4, base n = 2. The number m = 4 in base n = 2 requires 3 digits, thus a(14) = 3. (End)
MATHEMATICA
Table[Function[k, If[k == 1, m, IntegerLength[m, k]]][k - m + 1], {k, 13}, {m, k}] // Flatten (* Michael De Vlieger, Aug 31 2017 *)
CROSSREFS
KEYWORD
AUTHOR
Leroy Quet, Jul 01 2009
STATUS
approved